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   <div id="projectname">Optimist Racing
   &#160;<span id="projectnumber">0.1</span>
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   <div id="projectbrief">A video game where you must literally keep your head up</div>
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<div class="title">Bezier.hpp</div>  </div>
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<a href="_bezier_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/*  Copyright (C) 2012  Claude Richard</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> *  This program is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> *  it under the terms of the GNU General Public License as published by</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> *  the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> *  (at your option) any later version.</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> *  This program is distributed in the hope that it will be useful,</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"> *  but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"> *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment"> *  GNU General Public License for more details.</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> *  You should have received a copy of the GNU General Public License</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> *  along with this program.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">/* This file contains definitions for Bernstein polynomials,</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment"> * a specific type of Bezier patches,</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment"> * and grids of the above type of Bezier patches.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#pragma once</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#include &quot;<a class="code" href="_algebra_8hpp.html">Algebra.hpp</a>&quot;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">// Stores information about all the (D+1) Berstein polynomials of degree D (denoted Bi(t) for i=0 to D),</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">//   so you can use this object to efficiently compute their values and derivatives at arbitrary values of t.</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">// NOTE: The coefficient in front of each polynomial is 1, we&#39;re not using the Pascal triangle thing in this object.</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"><a class="code" href="class_bernstein_polynomial.html">   28</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;{</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <a class="code" href="class_bernstein_polynomial.html#a518fdef975c92857e34fa17077b0351a">BernsteinPolynomial</a>( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> degree );</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <a class="code" href="class_bernstein_polynomial.html#a9b74fd40365e53a1a0fd7de30d688ce0">~BernsteinPolynomial</a>();</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="comment">// Returns the degree of the polynomial</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_bernstein_polynomial.html#af121be73ab75d393d0344311810a9f66">getD</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="comment">// Returns a matrix of values and derivatives of each polynomial.</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="comment">// First index  i = which polynomial.               From 0 to D</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="comment">// Second index j = how many times differentiated.  From 0 to D</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> <a class="code" href="class_bernstein_polynomial.html#ae4dc99cf3e2ea03671ca459dffa02314">compute</a>( <span class="keywordtype">double</span> t ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="comment">// For this one, it only returns the first column of the above matrix.</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> <a class="code" href="class_bernstein_polynomial.html#a0f7c4c41e6c7d6258eac0ca090a621ea">computeFOnly</a>( <span class="keywordtype">double</span> t ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="comment">// highest power of t in the expression of B(t)</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> mD;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="comment">// This is like a 3-d array. The coefficients are all integers.</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="comment">// First index  i = which of the mDegree polynomials.   From 0 to D</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="comment">// Second index j = power of t.                         From 0 to D-i</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="comment">// Third index  k = power of (1-t).                     From 0 to i</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="comment">// The number of times differentiated is implied by the three indices.</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="comment">// The indices used in the implementation are are i, j*(i+1)+k</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keywordtype">int</span>** mB;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;};</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="comment">// This is a function f(x,y) for x,y from 0 to 1.</span></div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="comment">// The matrix K has all the coefficients.</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="comment">// f(x,y) = sum(over i and j)( Bi(x)*Bj(y)*Kij )</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="comment">//   where B are degree (2n-1) Bernstein Polynomials</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"><a class="code" href="class_bezier_patch.html">   60</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_bezier_patch.html">BezierPatch</a></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;{</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="comment">// K will be all zero in this constructor.</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <a class="code" href="class_bezier_patch.html#a50506bb4f40a7a537637a114a77d844e">BezierPatch</a>( <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* BP );</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="comment">// The argument matrices have to be in accordance with the specified n.</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <a class="code" href="class_bezier_patch.html#a50506bb4f40a7a537637a114a77d844e">BezierPatch</a>( <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* BP, <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> K );</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="comment">// Specify the value and some first, second etc derivatives at each corner.</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="comment">// Each matrix has the same format as the F returned in compute(x,y).</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="comment">// BP must have an odd degree so K can be a 2n*2n matrix, where 2n=D+1.</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="comment">// BTildaInv0 is the relevant quarter of BTilda0^-1. Same for BTildaInv1.</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <a class="code" href="class_bezier_patch.html#a50506bb4f40a7a537637a114a77d844e">BezierPatch</a>( <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* BP,</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;                 <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; BTildaInv0,</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;                 <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; BTildaInv1,</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;                 <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; f00, <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; f01,</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                 <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; f10, <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; f11 );</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <a class="code" href="class_bezier_patch.html#aefc712578c4818d622d8a9f623786746">~BezierPatch</a>();</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    </div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="comment">// Returns mK (see below)</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keyword">const</span> <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>&amp; <a class="code" href="class_bezier_patch.html#a32759c1605c0bd966ce87b6cf65bdd8f">getK</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="comment">// Returns the Berstein polynomial object that this uses.</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* <a class="code" href="class_bezier_patch.html#ab5ae6752b90f10228c98948d1184a1bb">getBP</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="comment">// x and y should both be between 0 and 1.</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="comment">// Returns the value and some derivatives of f at (x,y).</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="comment">// For example, when n = 2, it returns</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="comment">//   [ f, fy, fyy, fyyy;</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="comment">//     fx, fxy, fxyy, fxyyy;</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="comment">//     fxx, fxxy, fxxyy, fxxyyy;</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="comment">//     fxxx, fxxxy, fxxxyy, fxxxyyy ]</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> <a class="code" href="class_bezier_patch.html#a850bc5e09dfc474180f4bda49ddb6141">compute</a>( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="comment">// Returns the topleft value in the above matrix.</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="comment">// computeFOnly(x,y) is more efficient than compute(x,y).</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="class_bezier_patch.html#af70a22fab5c247edfa5b5b2a762dac4c">computeFOnly</a>( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* mBP;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> mK; <span class="comment">// K[i][j] = coefficient for Bi(x)*Bj(y)</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;};</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment">// This represents a grid where each cell is a BezierPatch.</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="comment">// Let 2n-1 = degree of the BernsteinPolynomial.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="comment">// Then the whole grid will be a function f:R^2-&gt;R</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="comment">//   that is C^n (differentiable n times) everywhere</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="comment">//   including on the edges between cells.</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="code" href="class_bezier_patch_grid.html">  105</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_bezier_patch_grid.html">BezierPatchGrid</a></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;{</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="comment">// corners is ordered in x = 0 to numCellsX-1, then by y.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="comment">//   so corners[2] can mean x=2,y=0</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="comment">// In this constructor, BP must have odd degree.</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <a class="code" href="class_bezier_patch_grid.html#a554a55115356412abc18baec436188be">BezierPatchGrid</a>( <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* BP,</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                     <span class="keywordtype">double</span> gridHx, <span class="keywordtype">double</span> gridHy,</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;                     <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> numCellsX, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> numCellsY,</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;                     <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a>** corners );</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <a class="code" href="class_bezier_patch_grid.html#a2d05668c85a89cc22ecec7527dc61fb6">~BezierPatchGrid</a>();</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="class_bezier_patch_grid.html#a097dc86c745cf672dae184ba638a575f">getGridHX</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="class_bezier_patch_grid.html#a415ab4140e78d397cf102ec7a349c858">getGridHY</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_bezier_patch_grid.html#a68d5e67e34eb2290e3dc66aad978003a">getNumCellsX</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_bezier_patch_grid.html#a527f5f89d884c8c496b87cd733bd5e57">getNumCellsY</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keyword">const</span> <a class="code" href="class_bezier_patch.html">BezierPatch</a>&amp; <a class="code" href="class_bezier_patch_grid.html#a9e9c8bbdad683ca8a9afba393c105223">getPatch</a>( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> x, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> <a class="code" href="class_bezier_patch_grid.html#a255a33e2613464997d2afee32bc549ab">compute</a>( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="class_bezier_patch_grid.html#afa4d08b2c4e00e9e9a068b5bff86951f">computeFOnly</a>( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y ) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="keyword">const</span> <a class="code" href="class_bernstein_polynomial.html">BernsteinPolynomial</a>* mBP;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordtype">double</span> mGridHx;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <span class="keywordtype">double</span> mGridHy;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> mNumCellsX;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> mNumCellsY;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    <span class="comment">// 1D array of pointers internally, but representing a 2D-array.</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    <a class="code" href="class_bezier_patch.html">BezierPatch</a>** mPatches;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="comment">// This is used in the compute() function</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="keywordtype">int</span> mN;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <a class="code" href="class_matrix_mx_n.html">MatrixMxN</a> mGridHMatrix;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;};</div>
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